A preferred form of projection lenses for wide screen television is disclosed in U.S. Pat. Nos. 4,348,081, 4,300,817, and 4,526,442, all assigned to the assignee of the present application.
In these previous patents, the lens units have been referred to as groups which perform specified or distinct optical functions. However, in accordance with present United States Patent and Trademark Office requirements, the overall lens will be defined in terms of optical "units". It will be understood that the term "units" refers to one or more optical elements or components air spaced from another optical unit.
It is well known that a specified optical function(s) of a lens unit or group in an overall lens may be accomplished by using one element or component or more than one element or component dependent upon the correction or function desired. A decision as to whether one or more elements is used as a lens unit in an overall lens design may be based on various considerations, including but not limited to, ultimate performance of the overall lens, ultimate costs of the lens, acceptable size of the lens, etc. Accordingly, in the following specification and appended claims, the term "lens unit" refers to one or more lens elements or lens components which provide a defined optical function or functions in the design of the overall lens.
The lenses disclosed in the aforementioned patents generally comprise three lens units: from the image end a first lens unit, haing at least one aspheric surface, which serves as an aberration corrector; a second lens unit including a biconvex element which supplies all or substantially all of the positive power of the lens; and a third lens unit having a concave surface towards the image end of the lens, serving as a field flattener, and essentially correcting the Petzval curvature of the first and second groups.
The lenses, as disclosed, are designed for use with a surface of a cathode ray tube (CRT). The lenses of U.S. Pat. No. 4,300,817, utilizing a single biconvex element in the second lens unit, all have an equivalent focal length (EFL) of one hundred twenty-seven millimeters or greater, while the lenses of U.S. Pat. No. 4,348,081, which utilize a two-element second lens unit, including the biconvex element, may have an EFL reduced to eighty-five millimeters as designed for direct projection for a five inch diagonal CRT. The lenses described in U.S. Pat. No. 4,526,442 are designed to have a fold in the optical axis between the first and second lens units and have been designed so that the EFL is as low as one hundred twenty-six millimeters. These EFL's are also for CRT screens having a viewing surface with an approximate five inch diagonal.
Projection TV sets are rather bulky and have required high volume cabinets. One manner of reducing the cabinet size is to decrease the EFL of the projection lenses. This, of course, increases the field angle of the lens.
A further consideration is introduced wherein a spacing is provided between the phosphor screen of the CRT and the third lens unit of the projection lens. This spacing may be required for the inclusion of a liquid cooling material and a housing necessary to enclose the coolant against the face of the CRT. This additional spacing between the face of the CRT causes the third negative lens unit to contribute more negative power, which must be compensated by increased power in the positive second lens unit.
An effect of increasing the angular coverage of the lens as a result of decreasing the EFL, is that the aberrations become more difficult to correct. A single biconvex element second lens unit, as shown in the aforementioned patents, does not provide the lens designer adequate degrees of freedom to correct for the resulting astigmatism and distortion. By dividing the optical power of the second lens unit, as disclosed in U.S. Pat. No. 4,348,081, the EFL may be shortened. However, merely splitting the optical power of the second lens unit into two elements to obtain additional degrees of optical design freedom, does not provide acceptable contrast and resolution where the angular coverage of the projection lenses is required to be in excess of twenty-seven degrees, semi-field.
The EFL of the lens is a function of the total conjugate distance between the CRT and the display screen. This is shown by the relationship EQU OL=EFL(1+1/M)+EFL(1+M)
where OL is the overall conjugate distance of the system from object to image
EFL (1+M) is the distance from the image to the first principal point of the lens PA1 EFL (1+1/M) is the distance from the object to the second principal point of the lens and PA1 M is the magnification of the system expressed as the ratio of object height to image height. PA1 K.sub.y is the "aspheric optical power" or "AOP" at height y; PA1 C.sub.1y and C.sub.2y are the local curvatures of the first and the second surfaces of the element, respectively, at height y; PA1 n is the index of refraction of the material from which the lens element is made.
Therefore, in order to decrease the total distance between the CRT and the screen, it is necessary to reduce the EFL.
Projection lens of the overall type described have been designed with decreased EFL's by designing a more complex second lens unit split into more than one lens element as exemplified in the lenses disclosed in co-pending application Ser. Nos. 642,825 and 652,062, filed Aug. 21, 1984 and Sept. 19, 1984, respectively.
These designs are currently used on many wide screen projection television sets and may have an equivalent focal length as low as eighty millimeters. It will be understood that the EFL will be greater if there is a fold in the optical axis between the first and second lens units.
Co-pending application Ser. No. 776,140, filed Sept. 13, 1985, discloses a projection lens in which the EFL is reduced to less than sixty millimeters.
In lenses of the type disclosed in the previously mentioned patents, the conventional way to accomplish this is to use a retrofocus or inverted telephoto type of design. Generally stated, a retrofocus lens is one in which the back focal length (BFL) is greater than the equivalent focal length. Lenses of this type have a negative group on the object end followed by a positive group. In this construction a very wide angle of the object can be covered, but the second lens unit requires two elements.
To achieve the objects of this invention, the aspheric surfaces of the lens units and the field flattener lens unit must be configured to achieve the desired aberration correction. It is difficult to describe aspheric surfaces in paraxial powers, since the optical power of the lens elements will vary with height from the optical axis. Therefore, the term of "aspheric optical power" will be used to describe the variation of the power of the lens element as a function of the height from the optical axis at which this optical power is computed. We will define the "AOP" in the following way: EQU K.sub.y =(n-1)(C.sub.1y -C.sub.2y)
where
As can be seen, this formula is essentially a thin-lens formula for the optical power of the single lens element, except now it must be calculated not just on optical axis of the element, but at various heights from that axis. In addition to that, the surfaces and powers of the lens units having aspheric surfaces will be at least partially described in terms of "approximating or best fitting spheres" or in terms of optical power based on lens elements having "approximating or best fitting spherical surfaces".
Approximating or best fitting spherical surfaces with respect to aspheric surfaces are discussed in a paper entitled, "Minimax Approximation By A Semi-Circle", by Charles B. Dunham and Charles R. Crawford, published in the Society For Industrial And Applied Mathematics Journal, Vol. 17, No. 1, February, 1980, the disclosure of which is incorporated herein by reference.
An algorithm prepared by one of the authors of the above referenced paper for defining the approximation of best fit of spherical surfaces with respect to aspherical surfaces is hereinafter set forth.